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 A303351 Expansion of Product_{n>=1} (1 + 9*x^n)^(1/3). 2
 1, 3, -6, 57, -294, 1884, -13011, 95178, -712293, 5448495, -42444375, 335392941, -2681006280, 21639853488, -176113016241, 1443450932445, -11903668996713, 98695838478585, -822212761531101, 6878755556938029, -57767592614370576, 486792969548157129 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -1/3, g(n) = -9. In general, if h > 1 and g.f. = Product_{k>=1} (1 + h^2*x^k)^(1/h), then a(n) ~ -(-1)^n * c^(1/h) * h^(2*n-1) / (Gamma(1 - 1/h) * n^(1 + 1/h)), where c = Product_{k>=2} (1 + (-1)^k / h^(2*k-2)). - Vaclav Kotesovec, Apr 22 2018 LINKS Table of n, a(n) for n=0..21. FORMULA a(n) ~ -(-1)^n * c^(1/3) * 3^(2*n-1) / (Gamma(2/3) * n^(4/3)), where c = Product_{k>=2} (1 + 9*(-1/9)^k) = 1.09874828793226302381837574278380702... - Vaclav Kotesovec, Apr 22 2018 MAPLE seq(coeff(series(mul((1+9*x^k)^(1/3), k = 1..n), x, n+1), x, n), n = 0..25); # Muniru A Asiru, Apr 22 2018 MATHEMATICA nmax = 30; CoefficientList[Series[Product[(1 + 9*x^k)^(1/3), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 22 2018 *) PROG (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1+9*x^k)^(1/3))) CROSSREFS Expansion of Product_{n>=1} (1 + b^2*x^n)^(1/b): A000009 (b=1), A303350 (b=2), this sequence (b=3). Sequence in context: A003098 A045914 A370520 * A067610 A067609 A012473 Adjacent sequences: A303348 A303349 A303350 * A303352 A303353 A303354 KEYWORD sign AUTHOR Seiichi Manyama, Apr 22 2018 STATUS approved

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Last modified August 7 21:19 EDT 2024. Contains 375017 sequences. (Running on oeis4.)